4/5 of a tank was filled with water. When 150 was removed, there was 1/2 of its volume. Find the capacity of the tank.
Understand the Problem
The question describes a tank that was initially filled with water, then some of the water was removed, and we're given the fraction of the tank's volume that remains. The task is to determine the full capacity of the tank based on this information.
Answer
The capacity of the tank is $500$.
Answer for screen readers
The capacity of the tank is 500.
Steps to Solve
- Define the variable
Let $x$ be the capacity of the tank.
- Express the initial amount of water
Initially, the tank was $\frac{4}{5}$ full, so the amount of water was $\frac{4}{5}x$.
- Express the amount of water after removing 150
After removing 150, the tank had $\frac{1}{2}$ of its volume left, so the amount of water is $\frac{1}{2}x$.
- Set up the equation
The amount of water initially minus 150 equals the amount of water remaining.
$$ \frac{4}{5}x - 150 = \frac{1}{2}x $$
- Solve for x
Subtract $\frac{1}{2}x$ from both sides:
$$ \frac{4}{5}x - \frac{1}{2}x = 150 $$
Find a common denominator (10) and combine the $x$ terms:
$$ \frac{8}{10}x - \frac{5}{10}x = 150 $$
$$ \frac{3}{10}x = 150 $$
Multiply both sides by $\frac{10}{3}$:
$$ x = 150 \cdot \frac{10}{3} $$
$$ x = \frac{1500}{3} $$
$$ x = 500 $$
The capacity of the tank is 500.
More Information
The capacity of the tank is 500 (presumably in some unit of volume, like liters or gallons, but the units are not specified in the problem).
Tips
A common mistake is to incorrectly set up the equation. For example, some might add 150 instead of subtracting, or mix up the fractions. Another common mistake is to make errors when performing the fraction arithmetic.
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